How to change the code in Arduino with another Arduino?

All is depending on your concept.
Serial communication will need to modify the sketch in the first Arduino. It is a lot of programming. The communication and data processing must be included in new APP. Serial in not necesserily for such model. The I2C, ISP... can be used also but serial is relatively easy and with good range.
ISP communication, like programming the EEPROM with the second Arduino, always needs the reset = interrupt in work for the 1st Arduino. You need not extra HW. The Arduino is able to do this job.
I would go to serial, definitely.